[Paper Review] A Game-Theoretic Approach to Recommendation Systems with Strategic Content Providers

Omer Ben-Porat, Moshe Tennenholtz|arXiv (Cornell University)|Jun 4, 2018

Advanced Bandit Algorithms Research21 citations

TL;DR

This paper proposes the Shapley mediator, a game-theoretic recommendation system that ensures fairness and stability by using the Shapley value to compute optimal display probabilities for strategic content providers. It is the only mechanism that simultaneously satisfies fairness, stability (via pure Nash equilibrium), and economic efficiency, while running in linear time and outperforming traditional systems in user utility.

ABSTRACT

We introduce a game-theoretic approach to the study of recommendation systems with strategic content providers. Such systems should be fair and stable. Showing that traditional approaches fail to satisfy these requirements, we propose the Shapley mediator. We show that the Shapley mediator fulfills the fairness and stability requirements, runs in linear time, and is the only economically efficient mechanism satisfying these properties.

Motivation & Objective

• To address fairness and stability challenges in recommendation systems where content providers act strategically to maximize exposure.
• To identify limitations of traditional recommendation systems that fail to ensure fairness and equilibrium stability.
• To design a mechanism that satisfies fairness, stability, and economic efficiency in multi-stakeholder recommendation environments.
• To prove the Shapley mediator is the unique mechanism meeting all three criteria: fairness, stability, and efficiency.
• To demonstrate the Shapley mediator's computational tractability and superior user utility compared to traditional approaches.

Proposed method

• Models the recommendation system as a cooperative game where content provider payoffs are tied to user satisfaction.
• Applies the Shapley value as a fair allocation mechanism to determine optimal display probabilities for content providers.
• Proves the Shapley mediator has a potential function, ensuring convergence of better-response dynamics to a pure Nash equilibrium.
• Extends the model to handle personalized recommendations where each provider may offer multiple items, selecting the one maximizing user satisfaction.
• Uses a one-to-one mapping from item sets to resource intervals to model multi-item strategies within the game-theoretic framework.
• Employs numerical optimization to analyze user utility and the price of anarchy, showing the Shapley mediator maintains high user satisfaction.

Experimental results

Research questions

• RQ1 Can traditional recommendation systems ensure fairness and stability when content providers act strategically?
• RQ2 What mechanism design principles can guarantee fairness, stability, and economic efficiency in multi-stakeholder recommendation systems?
• RQ3 Is there a unique mechanism that satisfies fairness, stability, and efficiency simultaneously?
• RQ4 How does the Shapley mediator perform in terms of user utility compared to traditional systems?
• RQ5 What is the computational complexity of implementing the Shapley mediator in practice?

Key findings

• The Shapley mediator is the only mechanism that satisfies fairness, stability (via pure Nash equilibrium), and economic efficiency simultaneously.
• The Shapley mediator runs in linear time, making it computationally efficient despite the intractability of the Shapley value in general settings.
• The system ensures user utility is at least 56.8% of the optimal possible, implying a price of anarchy of at most 1.761.
• Numerical analysis confirms that user utility under the Shapley mediator exceeds 0.568n for any number of users n, indicating strong performance.
• The Shapley mediator maintains stability through a potential function, ensuring convergence of better-response learning dynamics to equilibrium.
• The mechanism remains valid and effective even when content providers can offer multiple items, with the Shapley value computation preserved under personalized selection.